Advertisement

On-the-fly Fluid Model Checking via Discrete Time Population Models

  • Diego Latella
  • Michele Loreti
  • Mieke MassinkEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9272)

Abstract

We show that, under suitable convergence and scaling conditions, fluid model checking bounded CSL formulas on selected individuals in a continuous large population model can be approximated by checking equivalent bounded PCTL formulas on corresponding objects in a discrete time, time synchronous Markov population model, using an on-the-fly mean field approach. The proposed technique is applied to a benchmark epidemic model and a client-server case study showing promising results also for the challenging case of nested formulas with time dependent truth values. The on-the-fly results are compared to those obtained via global fluid model checking and statistical model-checking.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baier, C., Haverkort, B., Hermanns, H., Katoen, J.P.: Model-Checking Algorithms for Continuous Time Markov Chains. IEEE Transactions on Software Engineering 29(6), 524–541 (2003). IEEE CSCrossRefzbMATHGoogle Scholar
  2. 2.
    Benaïm, M., Le Boudec, J.: A class of mean field interaction models for computer and communication systems. Performance Evaluation 65(11–12), 823–838 (2008)CrossRefGoogle Scholar
  3. 3.
    Bortolussi, L., Hillston, J.: Fluid model checking. CoRR abs/1203.0920 (2012), version 2, January 2013Google Scholar
  4. 4.
    Bortolussi, L., Hillston, J.: Fluid model checking. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 333–347. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  5. 5.
    Bortolussi, L., Hillston, J.: Checking individual agent behaviours in markov population models by fluid approximation. In: Bernardo, M., de Vink, E., Di Pierro, A., Wiklicky, H. (eds.) SFM 2013. LNCS, vol. 7938, pp. 113–149. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  6. 6.
    Bortolussi, L., Hillston, J., Latella, D., Massink, M.: Continuous approximation of collective system behaviour: A tutorial. Performance Evaluation 70(5), 317–349 (2013)CrossRefGoogle Scholar
  7. 7.
    Darling, R., Norris, J.: Differential equation approximations for Markov chains. Probability Surveys 5, 37–79 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Della Penna, G., Intrigila, B., Melatti, I., Tronci, E., Zilli, M.V.: Bounded probabilistic model checking with the mur\({\varphi }\) verifier. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312, pp. 214–229. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  9. 9.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6, 512–535 (1994)CrossRefzbMATHGoogle Scholar
  10. 10.
    Hayden, R.: Scalable Performance Analysis of Massively Parallel Stochastic Systems. Ph.D. thesis, Imperial College London, April 2011. http://pubs.doc.ic.ac.uk/hayden-thesis/
  11. 11.
    Hillston, J.: Fluid flow approximation of PEPA models. In: Proceedings of the Second International Conference on the Quantitative Evaluaiton of Systems (QEST 2005), pp. 33–43 (2005)Google Scholar
  12. 12.
    Kolesnichenko, A., de Boer, P.T., Remke, A., Haverkort, B.R.: A logic for model-checking mean-field models. In: DSN, pp. 1–12. IEEE (2013)Google Scholar
  13. 13.
    Kurtz, T.: Solutions of ordinary differential equations as limits of pure jump Markov processes. Journal of Applied Probability 7, 49–58 (1970)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Latella, D., Loreti, M., Massink, M.: On-the-fly fluid model checking via discrete time population models: Extended version. QUANTICOL TR-QC-08-2014 (2014). www.quanticol.eu
  15. 15.
    Latella, D., Loreti, M., Massink, M.: On-the-fly PCTL Fast Mean-Field Model-Checking for Self-organising Coordination. Science of Computer Programming. Elsevier (2015). http://dx.doi.org/10.1016/j.scico.2015.06.009
  16. 16.
    Latella, D., Loreti, M., Massink, M.: On-the-fly fast mean-field model-checking. In: Abadi, M., Lluch Lafuente, A. (eds.) TGC 2013. LNCS, vol. 8358, pp. 297–314. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  17. 17.
    Latella, D., Loreti, M., Massink, M.: On-the-fly probabilistic model-checking. In: Proceedings 7th Interaction and Concurrency Experience ICE 2014. EPTCS, vol. 166 (2014)Google Scholar
  18. 18.
    Le Boudec, J.Y., McDonald, D., Mundinger, J.: A generic mean field convergence result for systems of interacting objects. In: QEST 2007, pp. 3–18. IEEE Computer Society Press (2007). ISBN: 978-0-7695-2883-0Google Scholar
  19. 19.
    LeVeque, R.J.: Finite Difference Methods for Ordinary and Partial Differential Equations. SIAM (2007)Google Scholar
  20. 20.
    Tribastone, M., Gilmore, S., Hillston, J.: Scalable differential analysis of process algebra models. IEEE Trans. Software Eng. 38(1), 205–219 (2012)CrossRefGoogle Scholar
  21. 21.
    å Younes, H.L.S., Kwiatkowska, M., Norman, G., Parker, D.: Numerical vs. statistical probabilistic model checking: an empirical study. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 46–60. Springer, Heidelberg (2004) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Istituto di Scienza e Tecnologie dell’Informazione ‘A. Faedo’, CNRPisaItaly
  2. 2.Dip. di Statistica, Informatica, Applicazioni ‘G. Parenti’Università di FirenzeFirenzeItaly
  3. 3.IMT Advanced Studies LuccaLuccaItaly

Personalised recommendations